Make totative ratio exact

(or, as exact as possible within a float64 - I only do one float
division, and everything else is a uint, so I think this means I will
get the closest available float64 value every time)

2 files changed, 9 insertions, 17 deletions

diff --git a/factors/factors_test.go b/factors/factors_test.go
index 33727c0..b7f48b9 100644
--- a/factors/factors_test.go
+++ b/factors/factors_test.go
@@ -3,7 +3,6 @@ package factors
 import (
 	"fmt"
 	"maps"
-	"math"
 	"testing"
 )
 
@@ -59,18 +58,14 @@ func TestFactors(t *testing.T) {
 }
 
 var totativeRatioCases = map[uint]float64{
-	1:  1.0,
-	2:  0.5,
-	3:  2.0 / 3.0,
-	4:  0.5,
-	6:  1.0 / 3.0,
-	8:  0.5,
-	12: 1.0 / 3.0,
+	1:  1.0, 2:  0.5, 3:  2.0 / 3.0, 4:  0.5,
+	6:  1.0 / 3.0, 7:  6.0 / 7.0, 8:  0.5,
+	12: 1.0 / 3.0, 14: 3.0 / 7.0, 15: 8.0 / 15.0,
+	30: 4.0 / 15.0, 60: 4.0 / 15.0, 120: 4.0 / 15.0,
 }
 
 func TestTotativeRatio(t *testing.T) {
-	equals := func(a, b float64) bool { return floatEquals(a, b, 1e-15) }
-	tableTest(t, TotativeRatio, totativeRatioCases, equals, "TotativeRatio")
+	tableTest(t, TotativeRatio, totativeRatioCases, stdEquals, "TotativeRatio")
 }
 
 var factorScoreCases = map[uint]float64{
@@ -199,7 +194,3 @@ func setEquals[E comparable](a, b []E) bool {
 	}
 	return maps.Equal(aSet, bSet)
 }
-
-func floatEquals(a, b, maxDelta float64) bool {
-	return math.Abs(a-b) <= maxDelta*math.Max(math.Abs(a), math.Abs(b))
-}
diff --git a/factors/totative.go b/factors/totative.go
index 558f0f0..3a1f635 100644
--- a/factors/totative.go
+++ b/factors/totative.go
@@ -8,10 +8,11 @@ func TotativeRatio(n uint) float64 {
 	}
 
 	primeFactorization := PrimeFactorize(n)
+	num, denom := uint(1), uint(1)
 
-	totativeRatio := 1.0
 	for p := range primeFactorization.exponents {
-		totativeRatio *= float64(p - 1) / float64(p)
+		num *= p - 1
+		denom *= p
 	}
-	return totativeRatio
+	return float64(num) / float64(denom)
 }